scholarly journals pyLLE: A Fast and User Friendly Lugiato-Lefever Equation Solver

2019 ◽  
Vol 124 ◽  
Author(s):  
Gregory Moille ◽  
Qing Li ◽  
Lu Xiyuan ◽  
Kartik Srinivasan
Keyword(s):  
Programming Language ◽  
Frequency Comb ◽  
Mean Field ◽  
Dissipative Structures ◽  
Optical Systems ◽  
User Friendliness ◽  
Frequency Combs ◽  
Nonlinear Resonator ◽  
Comb Generation ◽  
Python Programming

The Lugiato-Lefever Equation (LLE), first developed to provide a description of spatial dissipative structures in optical systems, has recently made a significant impact in the integrated photonics community, where it has been adopted to help understand and predict Kerr-mediated nonlinear optical phenomena such as parametric frequency comb generation inside microresonators. The LLE is essentially an application of the nonlinear Schrodinger equation (NLSE) to a damped, driven Kerr nonlinear resonator, so that a periodic boundary condition is applied. Importantly, a slow-varying time envelope is stipulated, resulting in a mean-field solution in which the field does not vary within a round trip. This constraint, which differentiates the LLE from the more general Ikeda map, significantly simplifies calculations while still providing excellent physical representation for a wide variety of systems. In particular, simulations based on the LLE formalism have enabled modeling that quantitatively agrees with reported experimental results on microcomb generation (e.g., in terms of spectral bandwidth), and have also been central to theoretical studies that have provided better insight into novel nonlinear dynamics that can be supported by Kerr nonlinear microresonators. The great potential of microresonator frequency combs (microcombs) in a wide variety of applications suggests the need for efficient and widely accessible computational tools to more rapidly further their development. Although LLE simulations are commonly performed by research groups working in the field, to our knowledge no free software package for solving this equation in an easy and fast way is currently available. Here, we introduce pyLLE, an open-source LLE solver for microcomb modeling. It combines the user-friendliness of the Python programming language and the computational power of the Julia programming language.

scholarly journals Dynamics of microresonator frequency comb generation: models and stability

Nanophotonics ◽  
2016 ◽  
Vol 5 (2) ◽  
pp. 231-243 ◽  
Author(s):  
Tobias Hansson ◽  
Stefan Wabnitz
Keyword(s):  
Continuous Wave ◽  
Temporal Dynamics ◽  
Frequency Comb ◽  
Modulational Instability ◽  
Theoretical Models ◽  
Light Sources ◽  
Generation Process ◽  
Modal Expansion ◽  
Frequency Combs ◽  
Comb Generation

AbstractMicroresonator frequency combs hold promise for enabling a new class of light sources that are simultaneously both broadband and coherent, and that could allow for a profusion of potential applications. In this article, we review various theoretical models for describing the temporal dynamics and formation of optical frequency combs. These models form the basis for performing numerical simulations that can be used in order to better understand the comb generation process, for example helping to identify the universal combcharacteristics and their different associated physical phenomena. Moreover, models allow for the study, design and optimization of comb properties prior to the fabrication of actual devices. We consider and derive theoretical formalisms based on the Ikeda map, the modal expansion approach, and the Lugiato-Lefever equation. We further discuss the generation of frequency combs in silicon resonators featuring multiphoton absorption and free-carrier effects. Additionally, we review comb stability properties and consider the role of modulational instability as well as of parametric instabilities due to the boundary conditions of the cavity. These instability mechanisms are the basis for comprehending the process of frequency comb formation, for identifying the different dynamical regimes and the associated dependence on the comb parameters. Finally, we also discuss the phenomena of continuous wave bi- and multistability and its relation to the observation of mode-locked cavity solitons.

scholarly journals Normal-dispersion microresonator Kerr frequency combs

Nanophotonics ◽  
2016 ◽  
Vol 5 (2) ◽  
pp. 244-262 ◽  
Author(s):  
Xiaoxiao Xue ◽  
Minghao Qi ◽  
Andrew M. Weiner
Keyword(s):  
Velocity Dispersion ◽  
Frequency Comb ◽  
Group Velocity Dispersion ◽  
Research Area ◽  
Future Directions ◽  
Normal Dispersion ◽  
Frequency Combs ◽  
The Past ◽  
Dispersion Regime ◽  
Comb Generation

AbstractOptical microresonator-based Kerr frequency comb generation has developed into a hot research area in the past decade. Microresonator combs are promising for portable applications due to their potential for chip-level integration and low power consumption. According to the group velocity dispersion of the microresonator employed, research in this field may be classified into two categories: the anomalous dispersion regime and the normal dispersion regime. In this paper, we discuss the physics of Kerr comb generation in the normal dispersion regime and review recent experimental advances. The potential advantages and future directions of normal dispersion combs are also discussed.

scholarly journals Optical Frequency Comb Generation based on Erbium Fiber Lasers

Nanophotonics ◽  
2016 ◽  
Vol 5 (2) ◽  
pp. 196-213 ◽  
Author(s):  
Stefan Droste ◽  
Gabriel Ycas ◽  
Brian R. Washburn ◽  
Ian Coddington ◽  
Nathan R. Newbury
Keyword(s):  
Frequency Comb ◽  
Building Blocks ◽  
Laser Frequency ◽  
Optical Frequency ◽  
Laser Amplifier ◽  
Optical Frequency Combs ◽  
Frequency Combs ◽  
Comb Generation ◽  
Optical Frequency Metrology ◽  
Frequency Metrology

AbstractOptical frequency combs have revolutionized optical frequency metrology and are being actively investigated in a number of applications outside of pure optical frequency metrology. For reasons of cost, robustness, performance, and flexibility, the erbium fiber laser frequency comb has emerged as the most commonly used frequency comb system and many different designs of erbium fiber frequency combs have been demonstrated. We review the different approaches taken in the design of erbium fiber frequency combs, including the major building blocks of the underlying mode-locked laser, amplifier, supercontinuum generation and actuators for stabilization of the frequency comb.

scholarly journals Power-efficient generation of two-octave mid-IR frequency combs in a germanium microresonator

Nanophotonics ◽  
2018 ◽  
Vol 7 (8) ◽  
pp. 1461-1467 ◽  
Author(s):  
Yuhao Guo ◽  
Jing Wang ◽  
Zhaohong Han ◽  
Kazumi Wada ◽  
Lionel C. Kimerling ◽  
...  
Keyword(s):  
Pump Power ◽  
Frequency Comb ◽  
Wide Band ◽  
Power Efficient ◽  
Frequency Combs ◽  
Dispersion Engineering ◽  
High Pump Power ◽  
High Pump ◽  
Limited Power ◽  
Comb Generation

AbstractOctave-spanning frequency comb generation in the deep mid-infrared (>5.5 μm) typically requires a high pump power, which is challenging because of the limited power of narrow linewidth lasers at long wavelengths. We propose twofold dispersion engineering for a Ge-on-Si microcavity to enable both dispersion flattening and dispersion hybridization over a wide band from 3.5 to 10 μm. A two-octave mode-locked Kerr frequency comb can be generated from 2.3 to 10.2 μm, with a pump power as low as 180 mW. It has been shown that dispersion flattening greatly enhances the spectral broadening of the generated comb, whereas dispersion hybridization improves its spectral flatness.

scholarly journals Numerical Simulation of Mid-Infrared Optical Frequency Comb Generation in Chalcogenide As2S3 Microbubble Resonators

Photonics ◽  
2019 ◽  
Vol 6 (2) ◽  
pp. 55 ◽  
Author(s):  
Elena A. Anashkina ◽  
Maria P. Marisova ◽  
Arseny A. Sorokin ◽  
Alexey V. Andrianov
Keyword(s):  
Frequency Comb ◽  
Spectral Width ◽  
Optical Frequency Comb ◽  
Infrared Range ◽  
Optical Frequency ◽  
Mid Infrared ◽  
Frequency Combs ◽  
Dispersion Wavelength ◽  
Zero Dispersion Wavelength ◽  
Comb Generation

Mid-infrared optical frequency comb generation in whispering gallery mode microresonators attracts significant interest. Chalcogenide glass microresonators are good candidates for operating in the mid-infrared range. We present the first theoretical analysis of optical frequency comb generation in As2S3 microbubble resonators in the 3–4 μm range. The regime of dissipative soliton plus dispersive wave generation is simulated numerically in the frame of the Lugiato–Lefever equation. Using microbubble geometry allows controlling of the zero-dispersion wavelength and the obtaining of anomalous dispersion needed for soliton generation at the pump wavelength of 3.5 μm, whereas the zero-dispersion wavelength of the analyzed As2S3 glass is ~4.8 μm. It is shown that, for the optimized characteristics of microbubble resonators, optical frequency combs with a spectral width of more than 700 nm (at the level of −30 dB) can be obtained with the low pump power of 10 mW.

scholarly journals Динамика спектров квантово-каскадных лазеров, генерирующих частотные гребенки в длинноволновом инфракрасном диапазоне

2020 ◽  
Vol 90 (8) ◽  
pp. 1333
Author(s):  
В.В. Дюделев ◽  
Д.А. Михайлов ◽  
А.В. Бабичев ◽  
С.Н. Лосев ◽  
Е.А. Когновицкая ◽  
...  
Keyword(s):  
Quantum Cascade Lasers ◽  
Frequency Comb ◽  
Laser Generation ◽  
Infrared Range ◽  
Simultaneous Generation ◽  
Frequency Combs ◽  
Longitudinal Modes ◽  
Generation Mode ◽  
Comb Generation ◽  
Cascade Lasers

The studies of the spectral and dynamic characteristics of quantum-cascade lasers emitting in the long-wave infrared range are presented. It has been shown that lasers with a short resonator (~ 1 mm) generating frequency combs in a very wide spectral range. The dynamics of the the frequency comb generation mode was studied. It is shown that the intensity of the longitudinal modes of laser generation changes during the pump pulse. At the same time, simultaneous generation of all longitudinal modes of the frequency comb during flat part of the pumping pulse is observed.

scholarly journals Gain-through-filtering enables tuneable frequency comb generation in passive optical resonators

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Florent Bessin ◽  
Auro M. Perego ◽  
Kestutis Staliunas ◽  
Sergei K. Turitsyn ◽  
Alexandre Kudlinski ◽  
...  
Keyword(s):  
Frequency Comb ◽  
Laser Frequency ◽  
Optical Resonators ◽  
Experimental Result ◽  
Molecular Fingerprinting ◽  
Optical Frequency Combs ◽  
Frequency Combs ◽  
Elegant Method ◽  
A New Technique ◽  
Comb Generation

Abstract Optical frequency combs (OFCs), consisting of a set of phase-locked, equally spaced laser frequency lines, have enabled a great leap in precision spectroscopy and metrology since seminal works of Hänsch et al. Nowadays, OFCs are cornerstones of a wealth of further applications ranging from chemistry and biology to astrophysics and including molecular fingerprinting and light detection and ranging (LIDAR) systems, among others. Driven passive optical resonators constitute the ideal platform for OFC generation in terms of compactness and low energy footprint. We propose here a technique for the generation of OFCs with a tuneable repetition rate in externally driven optical resonators based on the gain-through-filtering process, a simple and elegant method, due to asymmetric spectral filtering on one side of the pump wave. We demonstrate a proof-of-concept experimental result in a fibre resonator, pioneering a new technique that does not require specific engineering of the resonator dispersion to generate frequency-agile OFCs.

scholarly journals From the Lugiato–Lefever equation to microresonator-based soliton Kerr frequency combs

2018 ◽  
Vol 376 (2135) ◽  
pp. 20180113 ◽  
Author(s):  
L. A. Lugiato ◽  
F. Prati ◽  
M. L. Gorodetsky ◽  
T. J. Kippenberg
Keyword(s):  
Pattern Formation ◽  
Continuous Wave ◽  
Laser Frequency ◽  
Dissipative Structures ◽  
Low Noise ◽  
Optical Systems ◽  
Frequency Synthesis ◽  
Frequency Combs ◽  
Optical Microresonators ◽  
On Chip

The model, that is usually called the Lugiato–Lefever equation (LLE), was introduced in 1987 with the aim of providing a paradigm for dissipative structure and pattern formation in nonlinear optics. This model, describing a driven, detuned and damped nonlinear Schroedinger equation, gives rise to dissipative spatial and temporal solitons. Recently, the rather idealized conditions, assumed in the LLE, have materialized in the form of continuous wave driven optical microresonators, with the discovery of temporal dissipative Kerr solitons (DKS). These experiments have revealed that the LLE is a perfect and exact description of Kerr frequency combs—first observed in 2007, i.e. 20 years after the original formulation of the LLE—and in particular describe soliton states. Observed to spontaneously form in Kerr frequency combs in crystalline microresonators in 2013, such DKS are preferred state of operation, offering coherent and broadband optical frequency combs, whose bandwidth can be extended exploiting soliton-induced broadening phenomena. Combined with the ability to miniaturize and integrate on-chip, microresonator-based soliton Kerr frequency combs have already found applications in self-referenced frequency combs, dual-comb spectroscopy, frequency synthesis, low noise microwave generation, laser frequency ranging, and astrophysical spectrometer calibration, and have the potential to make comb technology ubiquitous. As such, pattern formation in driven, dissipative nonlinear optical systems is becoming the central Physics of soliton micro-comb technology. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

scholarly journals Direct generation of optical frequency combs in χ(2) nonlinear cavities

Nanophotonics ◽  
2016 ◽  
Vol 5 (2) ◽  
pp. 316-331 ◽  
Author(s):  
Simona Mosca ◽  
Iolanda Ricciardi ◽  
Maria Parisi ◽  
Pasquale Maddaloni ◽  
Luigi Santamaria ◽  
...  
Keyword(s):  
Near Infrared ◽  
Frequency Comb ◽  
Early Stage ◽  
Optical Cavity ◽  
Theoretical Description ◽  
Optical Frequency Combs ◽  
Frequency Combs ◽  
Direct Generation ◽  
Comb Generation ◽  
Spectral Ranges

AbstractQuadratic nonlinear processes are currently exploited for frequency comb transfer and extension from the visible and near infrared regions to other spectral ranges where direct comb generation cannot be accomplished. However, frequency comb generation has been directly observed in continuously pumped quadratic nonlinear crystals placed inside an optical cavity. At the same time, an introductory theoretical description of the phenomenon has been provided, showing a remarkable analogy with the dynamics of third-order Kerr microresonators. Here, we give an overview of our recent work on χ(2) frequency comb generation. Furthermore, we generalize the preliminary three-wave spectral model to a many-mode comb and present a stability analysis of different cavity field regimes. Although our work is a very early stage, it lays the groundwork for a novel class of highly efficient and versatile frequency comb synthesizers based on second-order nonlinear materials.

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